How Do You Solve a Word Problem Using an Equation Where You're Multiplying Fractions?

Summary

'h' is a variable that stands for Brad's current height
He was 5 and 1/2 feet tall when he was 2/3 as tall as he is now
5 and 1/2 converts to 11/2
Multiply both sides by 3/2 to solve for 'h'
'h' is equal to 33/4 or 8 and 1/4
Plug in 8 and 1/2 for 'h' to check our answer

Notes

1. 'h' is a variable that stands for Brad's current height
1. 2/3 times 'h' is his height two years ago
2. The left hand side is 2/3 times 'h'
3. 'h' is a variable that stands for Brad's current height
1. 5 and 1/2 is his height two years ago
2. The right hand side is 5 and 1/2
1. The right hand side is 5 and 1/2, a mixed fraction
1. Multiply the whole number of 5 times the denominator of 2, and then add the numerator of 1
2. The result is the new numerator, 11
3. The denominator stays the same
1. Solving for 'h' just means that we have to get 'h' by itself and to one side
2. 'h' is a variable that stands for Brad's current height
1. Since we are multiplying 2/3 by 'h', we must divide by 2/3 to cancel out the multiplication
1. Since we are multiplying 2/3 by 'h', we must divide by 2/3 to cancel out the multiplication
2. Dividing by 2/3 is the same as multiplying by its reciprocal
3. The reciprocal of 2/3 is 3/2
4. 'h' is a variable that stands for Brad's current height
1. Multiply 11/2 by 3/2
2. Multiply the numerators to get 11 times 3, which is 33
3. Multiply the denominators to get 2 times 2, which is 4
4. The right hand side is 33 over 4
1. 33/4 is an improper fraction
1. 33 divided by 4 is equal to 8 with a remainder of 1
2. The 8 becomes the whole number of the mixed fraction
1. The remainder, 1, becomes the numerator of the mixed fraction
2. The denominator is the same as we had before, 4
1. Plug our answer 8 and 1/2 into the equation, and then see if it makes a true statement
1. Plug our answer 8 and 1/2 into the equation, and then see if it makes a true statement
1. We already know what improper fractions our mixed fractions are
2. 8 and 1/4 is equal to 33/4
3. 5 and 1/2 is equal to 11/2
1. Multiply 2/3 by 33/4
1. 2/3 times 33/4 is equal to 66/12
2. Multiply the numerators to get 2 times 33, which is 66
3. Multiply the denominators to get 3 times 4, which is 12
1. Reduce the left hand side
1. Reduce the left hand side
2. We can pull a 6 out of the numerator and denominator of 66/12
3. 6/6 is the same as 1, and the 6's cancel out
4. 66/12 reduces to 11/2
1. Since both sides are equal, plugging in our answer for 'h' gives a true expression
2. 'h' is a variable that stands for Brad's current height
1. h' is a variable that stands for Brad's current height, and we are working in feet
1. h' is a variable that stands for Brad's current height, and we are working in feet
2. Label our answer in feet

Brad is the Algebra High team's star player. 2 years ago, when Brad was two-thirds as tall as he is now, he was five and a half feet tall. How tall is Brad now?

Summary

Notes