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A proportion is when the cross product of two fractions are equal. Take two fractions. 3 /4 and 12/16. If you take the numerator of the first fractions, and multiply it by the denominator of the second fraction, and the denominator of the first fraction times the numerator of the second fraction the products will be equal. 3*16 = 48 and 4*12 =48
Proportions are handy to solve problems because one term of the proportion becomes the unknown value. You then can find the value of the unknown term with a cross product, and solving an equation.
A rule of thumb is to use the first piece of information as the numerator, ( top number) but as long as you set up each ratio with the same units on the top and bottom you will solve the problem correctly.
Proportion Word Problems
Soccer Players
The number of pizzas is unknown so it becomes the X
X
Soccer Players
Pizza
Soccer Players
Soccer Players
=
=
120
X
40
10
1200 = 40X
Example problem: Solving Proportions
Step 1 Set up two fractions set to each other, with one variable (unknown)
Step 2 Make sure you have the same units on the top (numerator) and bottom (denominator)
Example: 60 miles = x miles
1 hours 7 hours
Step 3 Cross multiply to solve, 60 * 7 = 1 * x x = 420 miles
Proportion word problems
Your turn .... Try these Proportion word problems, then watch the video for the answer
Proportion word problem 1.
Sandy reduced the size of a rectangle to a height of 4 in. What is the new width if it was originally 27 in wide and 12 in tall?
Sandy reduced the size of a rectangle to a height of 4 in. What is the new width if it was originally 27 in wide and 12 in tall?Proportion word problem 2. Janie bought 30 oranges for $15. How many oranges can Laura buy if she has $6?
Janie bought 30 oranges for $15. How many oranges can Laura buy if she has $6?Proportion word problem 3. Juan took a trip to Mexico. Upon leaving he decided to convert all of his pesos back to dollars. How many dollars did he receive if he exchanged 110 Pesos at a rate: $ .75 = 10 Pesos?
Juan took a trip to Mexico. Upon leaving he decided to convert all of his pesos back to dollars. How many dollars did he receive if he exchanged 110 Pesos at a rate: $ .75 = 10 Pesos? Click the blue arrows for a new proportion word problem
Pizza
X
Common Core Standard: 6.RP.A1
30 pizzas = X
Video answer to all three proportion word problems
Solve this word problem involving proportions?
Suppose it takes 10 pizzas to feed a soccer team of 40 players, how many would it take to feed a team of 120 players?
Step 1. Set up a proportion.
Step 2. Set up a second ratio with the same information on the numerator and
denominator.
Step 3. Set these ratios equal and then cross multiply
Step 4. Solve for x
Directions
1. In order to view the answer check the " Solve Mathematical Thinking Box"
2. Next check the " Using the Model" "Using a Proportion" or the " Using a Table Box" or all three boxes in order to see the problem worked out.