Multiplication and Division of Rational Fractions

Harper, Charlotte, and Anika are having a friendly competition to see who can solve this problem the fastest: Multiply the rational fractions 7/8 and -2/3. Can you beat them to it?

• 5/6

• -7/12

• 1/6

• -14/24

Answer explanation

The question asks to multiply two fractions, 7/8 and -2/3. Multiplication of fractions is straightforward, you just multiply the numerators together for the new numerator and the denominators together for the new denominator. Doing so gives -14/24, which simplifies to -7/12, hence the correct answer.

Simplify the product of 3/4 and 5/6.

• 3/10

• 5/8

• 7/12

• 2/3

Answer explanation

The question asks to simplify the product of 3/4 and 5/6. The product of two fractions is obtained by multiplying the numerators together to get the new numerator and the denominators together to get the new denominator. So, (3/4) * (5/6) = 15/24, which simplifies to 5/8. Hence, the correct choice is 5/8.

Evaluate the division of 2/3 by 4/5.

• 1/2

• 8/15

• 10/12

• 6/7

Answer explanation

To solve the question, we need to divide 2/3 by 4/5. This is the same as multiplying 2/3 by the reciprocal of 4/5, which is 5/4. Multiplying these fractions together gives us 10/12, which is the correct answer.

Divide the mixed numbers 4 2/3 by 1 1/2.

• 10/3

• 5/6

• 3/2

• 28/9

Answer explanation

First, we need to convert the mixed numbers to improper fractions. 4 2/3 becomes 14/3 and 1 1/2 becomes 3/2. When we divide fractions, we multiply the first fraction by the reciprocal of the second. So, 14/3 divided by 3/2 becomes 14/3 * 2/3, which simplifies to 28/9. Therefore, the correct answer is 28/9.

Find the product.  Then, simplify.

• 10/18

• 5/9

• 10/6

• 15/12

Divide (it might be helpful to re-write this problem in the usual way you see dividing fractions) as 3/8 ÷ -1/7

• -21/8 or -2 ⅝

• -3/56

• 2 ⅝

• 3/56

Make sure your final answer is in simplest form.

Divide.

• -2/3

• 2/3

• -3/8

• 3/8

What is the quotient?
³/₄ ÷ ³/₈

• ¹/₂

• ¹/₄

• 0

• 2

Determine the quotient of -1.2 divided by 0.6.

• -0.5

• 1.2

• -2

• 2.4

Answer explanation

The question asks for the quotient of -1.2 divided by 0.6. The correct mathematical operation for this yields -2, which aligns with the correct choice. This operation is performed by dividing the dividend (-1.2) by the divisor (0.6).