Convert to. Fraction. Convert to. Decimal. Convert to. Percentage

Transcription

1 14 DECIMAL Divide the numerator by the denominator. When there is nothing left to bring down, add a decimal and zero PERCENTAGE Multiply by 100 and add a percent sign or SWOOPIE move the decimal two places to the right FRACTION Convert to Fraction Convert to Decimal PERCENTAGE 1. Divide numerator by denominator Multiply answer by 100 and add a percent sign x % Or SHWOOPIE move the decimal two places to the right FRACTION 1. Remove decimal point and write the number as the numerator The denominator is a multiple of 10, depending on the place value of the last digit Write the fraction and reduce to the lowest terms Divide the percentage by 100 and drop the percent sign. 12.5%.125 Or SHWOOPIE two steps to the left 2. Write the decimal as a fraction and reduce it to lowest terms Convert to Percentage DECIMAL 1. Divide the percentage by 100 and drop the percent sign. 12.5%.125 Or Swoopie two decimal places to the left

2 15 To turn a FRACTION into a DECIMAL, DIVIDE. Which number goes in the house? NUMERATOR No REMAINDERS. When you have nothing to bring down, add a DECIMAL and a ZERO! To write a FRACTION as a PERCENT, first turn it into a decimal, then move the decimal 2 times to the right. FRACTION TO DECIMAL To turn a DECIMAL into a PERCENT, move the DECIMAL two times to the RIGHT. O % To turn a PERCENT into a DECIMAL, move the DECIMAL two times to the LEFT. 50% % 6% % 200% 2.00 To write a DECIMAL as a FRACTION write the number over its place value To write a PERCENT as a FRACTION write it over 100, because percent means out of % %

3 16 DECIMAL METHOD: Change the PERCENT into a DECIMAL and then MULTIPLY! 46% of 120 PROPORTION STRATEGY: Part Percent Whole 100 Change the PERCENT into a DECIMAL 46% 0.46 EXAMPLE 46% of 120 Write a PROPORTION. X Multiply ( of means multiply in some cases) 120 x Don t forget to SHWOOP- Cross Multiply and Divide 100x X % STRATEGY: To find 71% of $80, first start by finding what 10% would be. 10% of $80 is $8 Move the decimal one place to the left to find 10% or divide by 10. 1% of $80 would be 0.8 Move the decimal two places to the left to find 1% or divide by 100. If 10% is $8, then 70% would be $56 (THINK: 7 times 8 56) 71% would be $56 + $0.80 or $56.80 (70% + 1% 71%) To find 25% of $48 10% of 48 is % of 48 is 9.6 (THINK: 2 times 4.8) 5% of 48 is 2.4 (THINK: half of 4.8) 25% of 48 is 12 (THINK: ) 20% + 5% TO FIND 10%, DIVIDE BY 10 (OR MOVE THE DECIMAL ONE PLACE TO THE LEFT!) FRACTION STRATEGY: STEP 1: Write the percent as a fraction. 20% of STEP 2: Multiply and simplify! x x

4 17 In Georgia, we have a 6% sales tax. You want to buy a shirt that costs $ How much does the shirt cost after taxes? COMMISSION: Cinthia earns 20% commission on her sales. In February, she sold $380 in merchandise. How much did Cinthia make in commission in February? STEP 1: Find TAX 6% Turn the percent into a decimal x STEP 2: Add TAX Original price Tax $12.72 TOTAL There are four decimal places in your problem, so the tax is 72 cents! $380 x 0.20 $76.00 She earned $76 in commission. INTEREST: Alberto s savings account earns 3% interest ever month. If Alberto puts $45.00 in his bank account at the beginning of the month, how much does he make in interest by the end of the month? $45.00 x 0.03 $1.35 Alberto earns $1.35 in interest. FINDING DISCOUNT (using decimal method): A shirt which regularly cost $45.00 is on sale for 20% off. What is the discount? 20% of $45 Change the PERCENT into a DECIMAL Multiply ( of means multiply in some cases) 20% of X $9.00 FINDING SALES PRICE (using decimal method): A shirt which regularly cost $45.00 is on sale for 20% off. What is the sales price? Find the DISCOUNT first Then subtract the discount from the original price Discount $ % of X $45-9 $36

5 23 KILO Kangaroos HECTO HOP DEKA DOWN BASE BANKS DECI DRINKING To convert move the decimal in the direction of the step you are moving to. For example: To change Meters to Centimeters move the decimal to the right 2 times. CENTI CHOCOLATE MILLI MILK 1) Write a ratio using the question. 2) Write the units by the ratio. 3) Write the ratio of the conversion. 4) Solve the proportion by cross multiplying, then dividing. X 10 pts How many inches are in 12 feet? X in 12 ft X in 12 in 12 ft 1 ft 1x X 144 X 30 yds CUSTOMARY SYSTEM: LENGTH: 1 foot 12 inches 1 yard 3 feet 1 mile 5,280 feet WEIGHT: 1 ton 2,000 lbs. 1 lb. 16 oz. CAPACITY (VOLUME): 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts METRIC SYSTEM: LENGTH: 1,000 mm 1 m 100 cm 1 m 1,000 m 1 km WEIGHT: 1,000 mg 1 g 1,000 g 1 kg CAPACITY (VOLUME): 1,000 ml 1 L

6 24 Similar Figures: Figures that are the same shape, but not always the same size The ratio of corresponding sides must be equal for the rectangles to be similar. 80 cm 30 cm 16 cm 6 cm CONGRUENT: Same shape, Same size 80 cm NOT SIMILAR: Scale factor: The ratio of corresponding sides for a pair of similar figures. Corresponding sides: Sides that have the same relative position on similar figures. Sides that match Example: Scale factor The triangles at right have a scale factor of 2, because the corresponding sides are 6 and The larger triangle is 2 times the size of the smaller triangle. 3 x 6 10 Step 1: Write a Proportion using corresponding parts (2nd Shape to 1st shape) Step 2: Cross Multiply and Divide to find the missing side 6x 6ft The missing side is 5 ft. The scale factor for the two triangles is 2, because So divide the side that corresponds to x, 10 ft, by 2. The missing side is 5 ft! 2 Sometimes the corresponding sides are rotated. 3 in corresponds to 6 in cdfdffdfsdfds 5 in corresponds to 10 in cdfdffdfsdfds 4 in corresponds to n in cdfdffdfsdfds

7 25 Scale Drawings- Drawings that represent real objects or places and are drawn to proportion Identify the drawing/model length and actual length. Write a ratio of the model over the drawing/model length to the actual length. The length of a car measures 240 inches. The length of the drawing is 12 inches. What is the scale factor of the drawing? The scale factor for the drawing of the car is 1:20, or one inch on the drawing represents 20 inches on the real car. Identify the scale. Set up a proportion with the scale on the left and the problem on the right. Set it up each ratio with the model or drawing to the real lengths. Avery has a model of a building for his architecture class. The model is 18 inches high. The scale factor of the model is 1:50. How many inches tall is the building that the model represents? 1 model 18 model 50 real x real 18 x 50 1x 900 1x 900 x The real building will be 900 inches. Use x to represent the length of the real building because this is the unknown value, or what we are solving to find! Identify the scale. Set up a proportion with the scale on the left and the problem on the right. Set it up each ratio with the model or drawing to the real lengths. Max is making a map of his hometown. The scale for the map will be 1 in on the map represents 3 miles. The distance between his house and his school is 4.5 miles. How far apart will Max need to draw his house and his school on the map? 1 in x in 4.5 3x The distance on the 3 miles 4.5 miles 3 3 map will be 1.5 inches. 1.5 x

8 26 Proportion- an equation that states that two ratios are EQUIVALENT X 3 X 3 We know these ratios are equal because 3 x 3 9 and 8 x The numerator and denominator are both multiplied by 3. 3 is the CONSTANT OF PROPORTIONALITY! When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. Question marks or letters are frequently used in place of the unknown number. To SOLVE a PROPORTION with an unknown, CROSS MULTIPLY and DIVIDE! n n 18 x 6 9 n 108 9n n n n x 3 9 n 81 9n n ANOTHER WAY IS TO LOOK FOR THE CONSTANT! 3 n 4 16 X 4 X 4 3 n 4 16 X 4 n 12 You can multiply 4 times 4 to get 16. So multiply 4 times 3 to get n 12! When you are given the value of two items which are related and then asked to figure out what will be the value of one of the item if the value of the other item changes, you have a proportional relationship! It is helpful to set up the ratios in words before using numbers so that you are consistent. Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 8 Tala for $2. How many Tala would she get if she exchanged $6? Tala Tala $ $ 8 x $2 $6 48 2x 24 x She will get 24 Tala. STEP 1: Underline keywords STEP 2: Set up ratios in WORDS. STEP 3: Plug in numbers. ( how many is represented by x) STEP 4: Solve proportion STEP 5: Check answer.

9 27 Coordinate plane- an area defined by the X AXIS and the Y AXIS. Points are plotted using coordinates from the ORIGIN. Using formulas to graph equations in the form y kx will help you see a relationship between two variables. The point (2,3) is OVER 2 and UP 3 from the ORIGIN. Graph the equation y 7 2 x X x 7 2 Y Tells how far over Tells how far up (or down) Direct Proportion: The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: AkB, where k is the constant of proportionality. Constant of Proportionality: In a proportional relationship, ykx, k is the constant of proportionality, which is the value of the ratio between y and x. MULTIPLIER CONSTANT: to find DIVIDE y x The equation below can be used to determine how many boys, y, are in a class that has x girls. 5 y x 6 If there are 12 girls in the class, how many boys are in the class? A. 8 B. 10 C. 12 D. 18 boys y 5 6 x 5 y y 6 y 10 boys girls STEP 1: Label variables STEP 2: Plug in what you know STEP 3: Solve STEP 4: Check answer.