Homework Headache: Solving Fractions Using Bar Graphs
Hi Homework Unlocked,
My whole family (husband, daughter and even our cat and dog 😉 are having trouble solving this problem. Could you give us a hand?
The Harrod Family
Not to worry, Homework Unlocked is here to help. We’ll walk you through this problem step by step so you can explain it to your daughter (plus your dog and cat!). This is a great example of a homework headache because it uses a bar diagram to solve a word problem with some algebra mixed in …phew!
Since we are given a partially completed bar diagram some of our work is already done for us, but we’ll start from the beginning so you can explain each step of solving fractions using bar graphs to your kids.
Step 1. When we start working with word problems read through them carefully and underline the relevant information.
Problem states: Of the beads in a box, ¼ are red. There are 24 more yellow beads than red beads. The remaining 76 beads are blue. How many beads are there altogether?
Step 2. Let’s work with each piece of underlined information to recreate the diagram from scratch.
A) ¼ of the beads are red: Simply draw a bar and shade a quarter of it in red.
B) There are 24 more yellow beads than red beads. We know that ¼ of the bead are red so color another ¼ in yellow and then mark 24 additional beads.
C) The remaining beads are blue- this is the easiest step, color all the remaining beads in blue.
D) Now we need to solve for the total number of beads
Step 3. Now that we can visualize the problem we can work on solving it. Looking at the problem we can easily see that ½ of the total beads equals 24 + 76, let’s write this out as an equation- we’ll represent the total number of beads with an X.
Now let’s solve for X to figure out how many beads we had total.
Now we need to isolate the X. To do this let’s get rid of the ½ by multiplying both sides of the equation by 2.
2/2 = 1 and we are left with X = 200
Step 4. Let’s check our work by solving for the number of beads in each color category.
We’re told ¼ of the beads are red. We now also know that the total number of beads = 200, therefore, there are 50 red beads. There are 24 more yellow beads than red beads, therefore, there are 50 + 24 = 74 yellow beads and 76 blue beads. If our work is correct these should add to make 200.
50 + 74 + 76 = 200 Our work checks!
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