Envision Math 2.0: Grade 7, Volume 1
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7. Multiply Rational Numbers
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Exercise 6 Page 48

When multiply real numbers, the product of an integer a by an integer b is always positive if those integers have the same sign. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) We want to find the given product. - 3.1 * (- 2.9) In this case both numbers are negatives, so the product will be positive. Before evaluate this expression, we will rewrite the decimal numbers as fractions. We will write fractions with 1 in the denominator.
- 3.1 * (- 2.9)
- 3.1 * 1/1 * - 2.9 * 1/1
- 3.1/1 * - 2.9/1
The calculations are easier if we multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. In this case, we will multiply by 10 the numerator and denominator of both fractions.
- 3.1/1 * - 2.9/1
- 3.1 * 10/1 * 10 * - 2.9* 10/1 * 10
- 31/10 * 29/10
Now that we have the fractions, we can evaluate the product. When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!
- 31/10*- 29/10
- 31* - 29/10* 10
31 * 29/10* 10
899/100
The product is 899100. We can also write this fraction as a mixed number.
899/100
800+99/100
800/100+99/100
8+99/100
8 99100
We want to find the given product. 1 12 * (- 5/3) Before evaluate the expression, will rewrite the mixed numbers as fractions.
1 12 * (- 5/3)
1* 2 +1/2 * (- 5/3)
2 +1/2 * (- 5/3)
3/2 * (- 5/3)
When multiply real numbers, the product of an integer a by an integer b is always positive if those integers have the same sign. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case one number is positive and one number is negative, so the product will be negative. Remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the product!
3/2 * (- 5/3)
3/2 * - 5/3
3* - 5/2* 3
- 3 * 5/2* 3
- 15/6
- 15/ 3/6/ 3
- 5/2
The product is 52. We can also write this fraction as a mixed number.
- 5/2
- 4-1/2
- 4/2-1/2
- 2 -1/2
- 2 12
We want to find the given product. - 3 12 * 0.5 Before evaluate the expression, will rewrite the mixed number as a fraction.
- 3 12 * 0.5
- 3* 2 +1/2 * 0.5
- 6 +1/2 * 0.5
- 7/2 * 0.5
Now, we will rewrite the decimal number as a fraction. To do so, we can start by writing a fraction with 1 in the denominator.
- 7/2 * 0.5
- 7/2 * 0.5 * 1/1
- 7/2 * 0.5/1
The calculations are easier if we multiply the divisor and the dividend by the same power of 10 so that the divisor is a whole number. In this case, we will multiply by 10 the numerator and denominator of 0.51.
- 7/2 * 0.5/1
- 7/2 * 0.5* 10/1 * 10
- 7/2 * 5/10
- 7/2 * 5/ 5/10/ 5
- 7/2 * 1/2
Now that we have the fractions, we can evaluate the product. When multiply real numbers, the product of an integer a by an integer b is always positive if those integers have the same sign. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case one number is positive and one number is negative, so the product will be negative. Remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the product!
- 7/2 * 1/2
- 7* 1/2* 2
- 7/4
The product is - 74. We can also write this fraction as a mixed number.
- 7/4
- 7/4
- 4-3/4
- 4/4-3/4
- 1 -3/4
- 1 34
We want to find the given product. - 4/5* - 1/8 When multiply real numbers, the product of an integer a by an integer b is always positive if those integers have the same sign. cc Same Sign & Different Signs (+)(+)=(+) & (+)(-)=(-) (-)(-)=(+) & (-)(+)=(-) In our case both numbers are negative, so the product will be positive. Remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the product!
- 4/5* - 1/8
4/5* 1/8
4* 1/5* 8
4/40
4/ 4/40/ 4
1/10