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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

1. Multiplying Fractions

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Exercise 53 Page 51

Rewrite the expression so that all terms are fractions. To multiply fractions, multiply both the numerators and the denominators.

No, see solution.

Practice makes perfect

We are told that our friend found the product of 2 12 and 7 45 with the given procedure.

We want to find if they are correct. Let's start by rewriting the expression so that all of its terms are fractions.

2 12 * 7 45

a bc=a* c+b/c

2* 2 + 1/2 * 7* 5+4/5

Multiply

4 + 1/2 * 35+4/5

Add terms

5/2 * 39/5

Now, recall that when multiplying fractions, the product is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

5/2 * 39/5

Multiply fractions

5* 39/2* 5

Multiply

195/10

a/b=.a /5./.b /5.

195÷ 5/10÷ 5

Calculate quotient

39/2

Finally, let's rewrite the answer as a mixed number and see if our friend was correct.

39/2

Rewrite 39 as 38+1

38+1/2

Write as a sum of fractions

38/2+1/2

Calculate quotient

19+1/2

Add terms

19 12

We found a different answer than our friend. Our friend is not correct because they multiplied the whole parts of each number separately from the fraction parts.

Extra

Distributive Property

We can speculate that our friend wanted to use the Distributive Property to evaluate the expression but they did it wrong. Remember that a mixed number a bc is the same as a + bc. With that in mind, let's use the Distributive Property to find the given product.

2 12 * 7 45

Rewrite 2 12 as 2+1/2

(2+1/2) * 7 45

Rewrite 7 45 as 7+4/5

(2+1/2) * (7+4/5)

Distribute (7+4/5)

2* (7+4/5) + 1/2* (7+4/5)

Distribute 2

2* 7+2 * 4/5 + 1/2* (7+4/5)

Distribute 1/2

2* 7+2 * 4/5 + 1/2* 7+ 1/2* 4/5

▼

Multiply

MoveLeftFacToNum

a*b/c= a* b/c

2* 7+ 2* 4/5 + 1/2* 7+ 1/2* 4/5

MoveRightFacToNum

a/c* b = a* b/c

2* 7+ 2* 4/5 + 1* 7/2+ 1/2* 4/5

Multiply fractions

2* 7+ 2* 4/5 + 1* 7/2+ 1* 4/2* 5

Multiply

14+ 8/5 + 7/2+ 4/10

a/b=a * 2/b * 2

14+ 8* 2/5* 2 + 7/2+ 4/10

a/b=a * 5/b * 5

14+ 8* 2/5* 2 + 7* 5/2* 5+ 4/10

Multiply

14+ 16/10 + 35/10+ 4/10

Add fractions

14+ 16+35+4/10

Add terms

14+ 55/10

a/b=.a /5./.b /5.

14+ 55÷ 5/10÷ 5

Calculate quotient

14+ 11/2

Rewrite 11 as 10+1

14+ 10+1/2

Write as a sum of fractions

14+ 10/2+1/2

Calculate quotient

14+ 5+1/2

Add terms

19+1/2

Rewrite 19+1/2 as 19 12

19 12

We can see that this is the same answer as we got by rewriting the mixed numbers as improper fractions, so we can be sure it is correct!

Subchapter links

Try It p.46-48

Self-Assessment for Concepts & Skills p.48

Self-Assessment for Problem Solving p.49

Review & Refresh p.50

Concepts, Skills, & Problem Solving p.50-52