# Improper Fractions and Mixed Numbers

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1 This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All work must be shown in order to earn full credit. The assignment will be graded for completion. REMEMBER: There are lots of ways of solving math problems. The suggested methods in this packet are just one way of solving the problem. If you have learned another method through your elementary math program that it is fine.

2 Improper Fractions and Mixed Numbers An improper fraction is a fraction with the numerator that is greater than the denominator. A mixed number is a whole number and a fraction. and 7 5 are improper fractions is a mixed number. An improper fraction can be written as a whole or mixed number. A mixed number can be written as a improper fraction. Write as whole Write 7 5 as a Write numbers. mixed numbers. as an improper fraction. Multiply the whole number by the denominator. Add this Divide the Divide the numerator by the product to the numerator. Then write the sum over the numerator by the denominator. Write the denominator. denominator. remainder as a fraction by writing the remainder over the 4 divisor = = = = 11 6 = = 11 6 Write as a whole number. 1) 16 4 = 2) 15 8 = ) 28 4 = 4) 48 6 = Write as a mixed number. 1) 15 4 = 2) 21 5 = ) 2 6 = 4) 7 2 = Write as an improper fraction. 1) 2 7 = 2) 8 1 = ) = 4) 2 5 =

3 Adding Mixed Numbers, Whole Numbers, and Fractions To add mixed numbers, whole numbers, and fractions, first check for unlike denominators. Write mixed numbers and fractions as equivalent fractions with like denominators. Add he fractions. Then add the whole numbers and simplify. Find: Write the fractions with Add the Add the whole Simplify. like denominators. fractions. numbers. 2 1 = = = = = = = 9 2 Add and simplify. 1) ) 1 4 ) 1 6 4) ) 1 6) ) 1 5 8)

4 Subtraction of Mixed Numbers with Regrouping To subtract mixed numbers, it may be necessary to regroup first. Write the whole number part as a mixed number. Add the mixed number and the fraction. Then subtract and simplify. Find: Write the fractions with like denominators. Compare the numerators. 5 7 = = is greater than 7. You cant subtract the fractions. To regroup, write 5 as the following mixed number. 5 = 4 Add the mixed number and the fraction. 5 7 = = 4 19 Now you can subtract and simplify. 5 7 = = 1 9 = 5 6 Subtract and Simplify. 1) 6 8 2) 7 4 ) ) ) )

5 Multiplication of Fractions To multiply fractions, multiply the numerators and multiply the denominators. Simplify the product. Find: 4 x 5 6 Multiply the numerators. Multiply the denominators. Simplify = 5 = = = = 5 8 Multiply and simplify. 1) 4 1 = 5 2) 1 = 5 ) 4 = 7 5 4) = 5) = 6) 1 11 = Multiplication of Whole Numbers by Fractions To multiply a whole number by a fraction, first write the whole number as an improper fraction. Multiply the numerators and the denominators. Simplify. Find: Write the whole number as an improper fraction = Multiply. Simplify. 6 5 = 0 = 1 14 = Multiply and simplify. 1) 2 6 2) 25 ) 25 5

6 Multiplication of Mixed Numbers by Whole Numbers To multiply a mixed number by a whole number, first write the mixed number and the whole number as improper fractions. Multiply the numerators and denominators. Simplify the answer. Find: Write the whole number and the mixed number as improper fractions = Multiply the numerators and denominators. Simplify. 9 4 = 6 = 4 4 = Multiply and Simplify. 1) = 2) 2 1 = ) = Multiplication of Mixed Numbers by Fractions To multiply a mixed number by a fraction, first write the mixed number as an improper fraction. Multiply the numerators and denominators. Simplify. Find: Write the mixed number as an improper fraction = Multiply the numerators and denominators. Simplify = 9 6 = 1 6 = Multiply and Simplify. 1) = 2) = ) =

7 Multiplication of Mixed Numbers by Mixed Numbers To multiply a mixed number by a mixed number, write both mixed numbers as improper fractions. then multiply the numerators and denominators. Simplify. Find: Write the mixed numbers as improper fractions. Multiply the numerators and denominators. Simplify = = 209 = 17 5 Multiply and Simplify. 1) = 2) = ) = 4) = 5) = 6) =

8 Division of Fractions by Fractions To divide a fraction by a fraction, multiply by the reciprocal of the second fraction. Simplify the answer if needed. Remember, only the second fraction is inverted. Find: Multiply by the reciprocal of the second fraction = Multiply the numerators and denominators. Simplify. 5 4 = 20 = Divide and Simplify. 1) 4 1 = 5 2) 5 1 = 4 ) 1 1 = ) = 5) = 6) = Division of Mixed Numbers by Fractions To divide a mixed number by a fraction, write the mixed number as an improper fraction. Multiply by the reciprocal of the second fraction. Simplify the answer. Find: Write the mixed number Multiply by the reciprocal Multiply and simplify. as an improper fraction. of the second fraction = = 40 = 4 = 1 4 Divide and Simplify. 1) = 2) = ) =

9 Fraction and Decimal Equivalents Sometimes you will need to either change a decimal to a fraction or fraction to a decimal. To write a decimal as a fraction, identify the value of the last place in the decimal. Use this place value to write the denominator. To write a fraction that has a denominator of, 0, or 1,000 as a decimal, write the digits for the numerator. Then write the decimal point. Decimal Fraction or Mixed Number Fraction or Mixed Number Decimal 0.7 = 7 9 = = 0.09 = 1.72 = ,000 or , or = 0.14 = 0.48 = 9.06 Write each decimal as a fraction. 1) 0.5 2) 0.06 ) ) 6.54 Write each decimal as a mixed number. 5) 2. 6) ) ) 7.5 Write each fraction as a decimal. 6) 9 7) 7 0 8) 9) 1 00 ) ) ) 17 1) 9 00

10 Addition and Subtraction of Decimals To add or subtract decimals, line up the decimal points. Write zeros as needed. Then add or subtract the same way as whole numbers. Examples: Find: Write a zero. Add. Write a decimal point in the sum. Find: Write a zero. Regroup. Subtract. Write a decimal point in the difference Add or subtract. Write zeros as needed

11 Multiplying Decimals by Decimals To multiply decimals by decimals, multiply the same way as whole numbers. Place the decimal point in the product by counting the number of decimal places in each factor. The product will have the same number of decimal places. Remember, sometimes you might need to write a zero in the product in order to place the decimal point correctly. Examples: Find: Multiply. Write the decimal point in the product. Find: Multiply. Write the decimal point in the product places + 1 place places Write a zero. 2 places + 2 places 4 places Multiply. Write zeros as needed

12 Dividing Decimals by Decimals To divide decimal by decimal, change the divisor to a whole number by moving the decimal point. Move the decimal point in the dividend the same number of places. Then divide. Remember, write a decimal point in the quotient directly above the position of the new decimal point in the dividend. Examples: Find: Move each decimal Divide. Find: Move each decimal Divide. point 1 place. point 2 places ) ) ) ) Divide ) ) ) ) ) )

13 Multiplying by Powers of To multiply decimals by powers of ten, move the decimal point in the product to the right as many places as there are zeros in the multiplier. Remember, sometimes you might need to write zeros in the product in order to move the decimal point the correct number of places. Study these examples. 0.2 = = 20 1, = = = 5.1 1, = 51 Multiply. Write zeros as needed = = ,000 = Dividing by Powers of To divide a decimal by a power of ten, move the decimal point in the dividend to the left as many places as there are zeros in the divisor. Remember, sometimes you might need to write zeros in the quotient in order to correctly insert the decimal point. Study these examples. 0.2 = = ,000 = = = ,000 = Divide. Write zeros as needed = = ,000 =

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