Multiplying Fractions

Which shows how the distributive property can be used to evaluate 7 x 8 4/5?

56 + 28/5 = 56 + 5 3/5 = 61 3/5

A leaky pool loses 2 1/4 inches of water each day. Jermaine and Mildred are asked to determine the change in the amount of water in the pool over 5 days. Jermaine's Solution Mildred's Solution 5(-2 1/4) 5(-2 1/4) 5(-2-1/4) 5(-2-1/4) -10-1/4 -10-5/4 -10 1/4 -11 1/4 Which describes the reasoning used to determine whose solution is correct?

Mildred is correct because she distributed 5 correctly.

Ivan and Polina have each drawn a conclusion about multiplying negative fractions. Ivan: The product of an even number of negative fractions is always positive. Polina: The product of an odd number of negative fractions is always negative. Whose conclusion is correct?

both Ivan and Polina

The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)?

(-1)(1/2)(-1)(1)

Which expression could be used to determine the product of -4 and 3 1/4?

(-4)(3) + (-4)(1/4)

Which could be used to evaluate the expression -6(4 2/3)?

(-6)(4) + (-6)(2/3)

Adante begins to evaluate the expression 31/3 x 5 1/4 using the steps below. 3 1/3 x 5 1/4 3 1/3 x (5+1/4) (3 1/3 x 5) + (3 1/3 x 1/4) (3 + 1/3)(5) + (3 + 1/3)(1/4) Which could be his next step?

(3)(5) + (1/3)(5) + (3)(1/4) + (1/3)(1/4)

Seven students cut 5 3/4 inches of thread from a spool for a school project. What number represents the change in the amount of the thread on the spool?

-40 1/4

Which is the best estimate of (-3/5)(17 5/6)?

-9

Which expression is the best estimate of the product of 7/8 and 8 1/10?

1 x 8

Yasmin purchased 6 heads of cabbage that each weighed 2 3/8 pounds. How much did the cabbage weigh all together?

14 1/4

Which is the best estimate of -14 1/9 (-2 9/10) ?

42

Calvin evaluated -2/3 x 5 1/6using the steps below. Step 1: -2/3 x (5 + 1/6) Step 2: (-2/3 + 5) x (-2/3 + 1/6) Step 3: 4 1/3 x -1/2 Step 4: -2 1/6 Which describes Calvin's error?

In step 2 he confused the multiplication and addition signs.

Nico and Lorena used different methods to determine the product of three fractions. Nico's Method Lorena's Method (2)(1/6)(-4/5) (2)(1/6)(-4/5) =(2/1)(1/6)(-4/5) =(2/1)(1/6)(-4/-5) =(2)(1)(-4)/(1)(6)(5) =(2)(1)(-4)/(1)(6)(-5) = -8/30 = -8/-30 = -4/15 = 4/15 Whose solution is correct and why?

Nico is correct because he knew that - 4/5 = -4/5

Vassil rounded to the nearest half to estimate the product of 5/8 and 8/9. How do the estimated and actual products compare? (Hint: use 18 for the denominator when estimating.)

The actual product is about 1/18 greater than the estimate.

Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8. How do the estimate and the actual product compare?

The actual product is greater than the estimate. The numbers differ by less than one.