7. [Decimals / Fractions / Percentages]

Transcription

1 7. [Decimals / Fractions / Percentages] Skill 7. Ordering decimal numbers. MM. MM. Line up the decimal numbers at their decimal points. Compare digits in the same places, starting from the left, until you find the smallest digit. Hint: The number with the smallest digit will be the smallest number. Look for the second smallest number. Continue in this way until you find the largest number. Q. Place in order from smallest to largest: 0., 0.0, 0.0, 0. units U. T (largest) th (smallest) st nd rd 0. HTh tenths hundredths thousandths A. 0.0, 0.0, 0., 0. Find the smallest digits. Work from left to right. Units: all 0 Tenths: 0 < < either 0.0 or 0.0 is the smallest Hundredths: < so 0.0 is the smallest and 0.0 is nd smallest Tenths: < so 0. is rd smallest 0. is the largest a) Place in order from smallest to largest: 0.0, 0., 0.0, 0.0 U. T HTh 0 the smallest number b) Place in order from largest to smallest:.0,.0,.0,.0 U. T HTh c) Write in ascending order: 0., 0., 0., 0. d) Write in descending order: 0.0, 0.0, 0.0, 0.0 e) Write in descending order: 0.07, 0.07, 0.70, 0.07 f) Write in ascending order:.,.0,.,. g) Write in ascending order: 0.7, 0.70, 0.07, 0.7 h) Write in descending order:.8,.8,.8,.8 page 7 Maths Mate./. Skill Builder 7

2 Skill 7. Ordering fractions. MM. MM. Find the lowest common denominator of the fractions, which is the Lowest Common Multiple (LCM) of the denominators. Change the fractions to equivalent fractions with the lowest common denominator. Arrange the fractions in order of the numerators (the smallest fraction has the smallest numerator and so on). Hints: If unsure which is the LCM of the denominators, use their product as the common denominator. When the smaller denominators divide evenly into the biggest denominator, this biggest number becomes the common denominator. 8 Q. Place in ascending order:, 8, 00 A. smallest numerator smallest fraction, 00,,, < < same denominator LCM of, and 00 is 00 because 00 because < 8 < 8, so < < or < 8 00 < a) Place in ascending order:,, < < LCM of, and 8 is c) Place in ascending order: 7,,,, 8 b) Place in descending order: 0,, d) Place in descending order: 7 7 0, 0, e) Place in ascending order: 0, 8,... f) Place in descending order: 7,, page 7 Maths Mate./. Skill Builder 7

3 Skill 7. Finding equivalent fractions. MM. MM. Check if you need to multiply or divide the numerator or denominator of the first fraction to reach the numerator or denominator of the second fraction. Do the same operation to the top and bottom of the fraction. Example:? 8 8 So and are equivalent fractions. 8 Multiply or divide the numerator and denominator of the first fraction by the same number until you reach the second fraction. 0 Q. Complete the equivalent A.? and 80? 80 0 a) Complete the equivalent 8? 8 d) Complete the equivalent b) Complete the equivalent 8 00 e) Complete the equivalent c) Complete the equivalent f) Complete the equivalent g) Complete the equivalent h) Complete the equivalent i) Complete the equivalent j) 0 0 True or false? true Simplify: Divide by 0 k) l) True or false? True or false? page 7 Maths Mate./. Skill Builder 7

4 Skill 7. Writing a decimal number as a percentage. MM. MM. Multiply the decimal number by 00, by moving the decimal point two places to the right. Add the percentage sign. Hint: Zeros can be added at the end of any decimal number: Q. Write 0. as a percentage. A %.% zeros, places to the right a) Write 0.0 as a percentage %... % b) Write 0. as a percentage. 0. c) Write 0. as a percentage. d) Write 0.88 as a percentage. e) Write 0.08 as a percentage. f) Write 0. as a percentage. g) Write 0.0 as a percentage. h) Write 0. as a percentage. i) Write 0. as a percentage. j) Write 0.0 as a percentage. k) Write 0.0 as a percentage. l) Write 0.07 as a percentage. m) Write. as a percentage. n) Write. as a percentage. o) Write. as a percentage. p) Write. as a percentage. q) Write 0. as a percentage. r) Write 0. as a percentage. page 7 Maths Mate./. Skill Builder 7

5 Skill 7. Writing a percentage as a decimal number. MM. MM. Write the percentage as a fraction out of 00. Divide the numerator of the fraction by 00, by moving the decimal point two places to the left. Hint: Fractions are just divisions. There is a decimal point and zeros which are not written, at the end of any whole number: Zeros can also be added before the number: Q. Write.% as a decimal number. A..% zeros, places to the left a) Write % as a decimal number. % c) Write 70% as a decimal number. e) Write 0% as a decimal number. g) Write.% as a decimal number. i) Write.% as a decimal number. 0.0 b) Write % as a decimal number. % d) Write 8% as a decimal number.. f) Write % as a decimal number. h) Write.% as a decimal number. j) Write.% as a decimal number. k) Income tax is % for an income between $00 and $ 00. Write the percentage as a decimal. m) The interest rate of a major credit card is 7.%. Write this as a decimal. l) Approximately 0% of the waste at the tip is household waste. Write this as a decimal. n) Maximum legal blood alcohol concentration for drivers in NSW is 0.0%. What is this as a decimal? page 7 Maths Mate./. Skill Builder 7

6 Skill 7. Writing a decimal number as a fraction in MM. MM. Write the decimal number as the numerator of the fraction. Ignore any zeros at the start of the number. Use the place value of the last digit of the decimal number to determine the size of the denominator. Example: units Hint: For the denominator, write followed by one zero for each digit after the decimal point. Example: Q. Write 0. as a fraction in tenths hundredths A Write the 8 as the numerator hundredths 8 8 in hundredths place, 00 denominator 00 Write the fraction in Divide both the numerator and the denominator by the same number. Example: 8 00 Simplify: 00 Write the as the numerator zeros for decimal places a) Write 0. as a fraction in Simplify: 0. 0 c) Write 0. as a fraction in 0. e) Write 0. as a fraction in g) Write 0. as a fraction in i) Write 0.8 as a fraction in b) Write 0.0 as a fraction in 0.0 d) Write 0.0 as a fraction in f) Write 0.8 as a fraction in h) Write 0.8 as a fraction in j) Write 0.0 as a fraction in page 7 Maths Mate./. Skill Builder 7

7 Skill 7.7 Writing a fraction as a terminating decimal. MM. MM. When the denominator is a power of 0: Divide the numerator by the power of 0 by moving the decimal point to the left. 7 Example: Hints: Fractions are just divisions. There is a decimal point and zeros which are not written, at the end of any whole number: Zeros can also be added before the number: The number of zeros in the denominator shows the number of digits after the decimal point zeros, places to the left When the denominator is not a power of 0: EITHER Multiply both the numerator and denominator by the same number to make the denominator a power of 0. (e.g. 0, 00 or 000). Example: OR Divide the numerator by the denominator. Example: power of 0 Hint: Fractions are just divisions. Q. Write as a decimal. a) Write as a decimal d) Write as a decimal. 0 g) Write as a decimal. Make denominator a power of A b) Write as a decimal. 0 h) Write as a decimal. 0 0 because 00 0 e) Write as a decimal. zeros, places to the left OR A c) Write as a decimal. f) Write as a decimal. i) Write as a decimal. 0 page 77 Maths Mate./. Skill Builder 7

8 Skill 7.8 Writing a percentage as a fraction in MM. MM. Write the percentage as a fraction with the denominator of 00. Simplify the fraction by dividing both the numerator and the denominator by the same number. Hints: Percent means per hundred or out of a hundred. A percentage is another way of writing a fraction out of one hundred. Example: 7% is said 7 percent and means 7 out of 00. Q. Write 8% as a fraction in A. 8% 8 00 Simplify: a) Write % as a fraction in % Simplify: 00 c) Write 7% as a fraction in e) Write 8% as a fraction in g) Write % as a fraction in i) Write 0% as a fraction in k) If Australia s Gross National Product grew % quarterly in 00, what would the percentage be if written as a fraction in simplest form? m) If % of women have obtained a bachelor degree, what would the percentage be if written as a fraction in simplest form? b) Write % as a fraction in % d) Write 0% as a fraction in f) Write 0% as a fraction in h) Write % as a fraction in j) Write % as a fraction in l) A 00 survey found that 7% of teenagers owned an MP player or an ipod. Write this percentage as a fraction in n) A 0 survey found that % of people give to charity once a month. Write this percentage as a fraction in page 78 Maths Mate./. Skill Builder 7

9 Skill 7. Number 00 Writing a fraction as a percentage. EITHER Find the equivalent fraction which has a denominator of 00. The numerator of this fraction becomes the equivalent percentage. Example: Number % % Fraction 00 % Percentage OR 00 Multiply the fraction by and include the % sign. 00 Example: % 0 0 0% MM. MM. Simplify: 0 Q. What percentage is out of? A % 0 0 because 00 0 OR A % 0% 0% Simplify: a) Write as a percentage % 7 b) Write as a percentage c) Write as a percentage. d) Write as a percentage. 70 e) What percentage is out of 0? f) What percentage is out of 0? 00 % % 0 0 g) Ng receives $0 commission on a $000 sale. What percentage is this? h) In a class of students, 0 play netball. What percentage is this? i) One quarter of the men surveyed enjoy walking as their main form of physical exercise. What percentage is this? j) Three tenths of the women surveyed enjoy aerobics/fitness as their main form of physical exercise. What percentage is this? page 7 Maths Mate./. Skill Builder 7

10 Skill 7.0 Converting between decimals, fractions and percentages. MM. MM. numerator by denominator 00% make denominator 00 and simplify Decimals Percentages Fractions 00% 00 % For denominator put followed by one zero for each digit after the decimal point and simplify Q. Complete the table: Decimal Fraction Percentage % A. % 00 0 % Simplify: zeros, places to the left Fraction Decimal Decimal Fraction Percentage % a) Complete the table: Decimal Fraction Percentage 0.0 b) Complete the table: Decimal Fraction Percentage 0.7 Simplify: %.% c) Complete the table: d) Complete the table: Decimal Fraction Percentage Decimal Fraction Percentage page 80 Maths Mate./. Skill Builder 7

11 Skill 7. Finding a fraction of a whole number. MM. MM. EITHER Change of to. Multiply the fraction by the whole number. (see skill., page ) Cross simplify where possible before multiplying. (see skill., page ) OR Divide the whole number by the denominator of the fraction. Multiply the result by the numerator of the fraction. Example: Three fifths of 0? First find one fifth of 0 by dividing 0 by : 0 Then find three fifths of 0 by multiplying by. + + So three fifths of 0 is. Q. Of the 00 seats in the Opera Theatre at Sydney Opera House in Sydney, five sixths were occupied. How many spectators were in the Opera Theatre? A. 0 of Simplify: To find of a number of a number of a number of a number of a number of a number 0 0 and so on. OR A Find 0 0 Find a) Find of 0. Simplify: 0 0 of c) Find of 0. e) Of the 0 European countries, have German as their official language. How many European countries have German as their official language? g) Of the medals won by New Zealand at the 00 Commonwealth Games, one sixth were gold. How many gold medals did New Zealand win? i) Two fifths of the $00 raised at the Fireworks Frenzy were from the entry tickets. How much money was raised from the tickets?... $ b) Find four sevenths of 80. d) Find five eighths of 00. f) The Western Bulldogs won four elevenths of the games played in the 0 AFL season. How many games did the Western Bulldogs win? h) Only one tenth of the 0 qualifiers at the American Idol are chosen for the finals. How many will sing in the finals? j) Maria paid one twentieth of $0 000 as a deposit for a house. How much did she pay up-front?... $ page 8 Maths Mate./. Skill Builder 7

12 Skill 7. Comparing and ordering decimals, fractions and percentages. MM. MM. Convert the decimals, fractions and percentages to the same form, by writing all as decimals, or as fractions, or as percentages. (see skill 7., page 8) Compare and order the decimals, or the fractions, or the percentages. Hint: The most convenient form is the decimal form. Write the fractions and percentages as decimals. Q. Write in ascending order: 7, 0.7, 7% 00 a) Which is greater? 0.0 or 0% 0 0% > 0.0 c) Place in ascending order:, 0., 0% Fraction Percentage % < 0. < % 7 A % The order from smallest to largest is: , 0.7, 0.7 OR 7%,, b) Which is greater? 0.8 or 7%... d) Place in descending order: 0., %, 0 Fraction Percentage Write the fraction as a decimal zeros, places to the left Write the percentage as a decimal Fraction Percentage e) Place in ascending order:, 0., % Percentage Fraction......,... f) Place in descending order:, 0.8, 8% Fraction Percentage page 8 Maths Mate./. Skill Builder 7

13 Skill 7. Recognising expanded form for recurring decimals. MM. MM. If the dot is above one digit Write the digit repeatedly. If the dots are above two digits side by side Write the group of digits repeatedly. If the dots are above two digits which are not side by side Write the group of all the digits in between the dots repeatedly. Q. 0. is the notation for: A ) 0... B ) 0... C ) 0... A. B The dots above (side by side) mean that must be repeated indefinitely after. a) 0. is the notation for: A ) B ) 0... C )... B b). is the notation for: A ).0... B ) 0... C )... c). is the notation for: A )... B )... C ) 0... d) 0.7 is the notation for: A ) B ) C ) e) 0.7 is the notation for: A ) B ) C ) f) 0.8 is the notation for: A ) B ) C ) g) 0. is the notation for: A ) 0... B ) 0... C ) 0... h) 0. is the notation for: A ) 0... B ) 0... C ) 0... i) 0. is the notation for: A ) 0... B ) 0... C ) 0... j) 0.7 is the notation for: A ) B ) C ) page 8 Maths Mate./. Skill Builder 7

14 Skill 7. Writing a fraction as a recurring decimal. MM. MM. Divide the numerator by the denominator. Write a decimal point and zeros at the end of the numerator to complete the division. In the result, when a single digit is repeating after the decimal point, write the digit only once with a dot on top. In the result, when a pattern of digits is reapeating after the decimal point, write the pattern only once, with a dot over the first and last digit of it. Examples: OR OR OR OR Q. Write as a recurring decimal. A a) Write as a recurring decimal b) Write as a recurring decimal c) Write as a recurring decimal. d) Write as a recurring decimal e) Write as a recurring decimal. f) Write as a recurring decimal page 8 Maths Mate./. Skill Builder 7

15 Skill 7. Writing a recurring decimal as a fraction. MM. MM. Convert each fraction to a decimal to find the answer. (see skill 7., page 8) Q. Which fraction does 0. equal? A ) B) C) 00 A. A) B) C) The answer is C. a) Which fraction is approximately equal to 0.? A ) B) C) c) Which fraction does 0. equal? A ) B) C) 0 b) Which fraction does 0. equal? A ) B) C) d) Which fraction does 0.08 equal? A ) B) C) e) Which fraction does 0. equal? A ) B) C) 0 00 f) Which fraction does 0.7 equal? A ) B) C) page 8 Maths Mate./. Skill Builder 7

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