Answer:
First, we know two things:
length = 2 1/2 m
length = 1 9/16 * width
We can rewrite the second equation as 2 1/2 = 1 9/16 * w
So we need to figure out what number times 1 9/16 gives us 2 1/2.
We don’t want to guess and check that.
What operation is the opposite of multiplication? Division.
Think about a fact family. The two smaller numbers multiply to the bigger number. The biggest number divided by one of the smaller number equals the other smaller number
(ie 3*4 = 12; 4*3 = 12; 12 ÷ 3 = 4; 12 ÷ 4 = 3)
So we can say that 2 1/2 ÷ 1 9/16 = width
Change these to improper fractions:
5/2 ÷ 25/16 = width
To divide fractions, use KEEP- CHANGE- FLIP. Keep the first fraction the same, change divide to multiply, and flip the second fraction:
5/2 * 16/25 = width
To multiply fractions, multiply the numerators (the tops) together and multiply the denominators (the bottoms) together. Multiply straight across.
5*16 = 80
2*25 = 50
80/50 = width
Simplify:
10 can divide evenly into both 50 and 80
So we get 8/5 = width
Use long division to change that back to a mixed number:
1 3/5 meters = width
Now V = l*w*h
12 3/4 = 2 1/2 * 1 3/5 * height
Change all of the fractions to improper fractions:
51/4 = 5/2 * 8/5 * h
Multiply 5/2 * 8/5 = 40/10 = 4
So
51/4 = 4 * h
Use the opposite operation like we did earlier. Instead of thinking what times 4 = 51/4, divide:
51/4 ÷ 4 = h
51/4 * 1/4 = h
51/16 = h
Use long division to change that back to a mixed number:
3 3/16 meters = h