6th Grade Math: Help with Ratios and Rates

In 6th grade, you'll learn about ratios and unit rates, and you'll use them to solve different types of problems. Keep reading for explanations and helpful examples!

Find available tutors

Ratio and Rate Help

What's a Ratio?

A ratio expresses the relationship between 2 related amounts. For instance, in a recipe, the amount of each ingredient that you add is related to the amounts of the other ingredients used. If you're making bread that has 2 cups of flour and 1 cup of water, you could write this as the ratio 2:1 (2 to 1). This information is helpful if you wanted to double the recipe because you'd know that if you doubled the flour to 4 cups, you'd also need to double the water to 2 cups.

Ratios are used in lots of other situations as well. For example, imagine that you're given a picture containing 2 triangles and 7 circles, and asked to write the ratio of triangles to circles. You'd simply count the number of each type of shape and write the ratio, which is 2:7. If you'd been asked to write the ratio of circles to triangles instead, it would be 7:2.

It's important to note that ratios can also be written as fractions. For instance, 2:7 would be 2/7 and 7:2 would be 7/2. You'll see why this is critical in the next section.

Understanding Unit Rates

You can think of a unit rate as yet another way of expressing a ratio. To calculate a unit rate, write the ratio as a fraction, and then divide the top number by the bottom number. This will tell you how many of the units on top there are for each bottom unit.

Let's use an example to make this a bit more concrete. Going back to the triangles and circles, recall that we said the ratio of triangles to circles was 2:7 or 2/7. To find the unit rate, solve 2 ÷ 7 to get a decimal that rounds to 0.3. This means there are about 0.3 triangles for every 1 circle.

You can also reverse this by stating the unit rate in terms of the ratio of circles to squares (7:2 or 7/2). Since 7 ÷ 2 = 3.5, you can also say there are 3.5 circles for every 1 triangle.

Unit rates are commonly used for situations that involve rates of speed. For instance, let's say you can ride your bike 20 miles every 2 hours, which can be represented by the ratio 20:2. To find the unit rate of speed in miles per hour (mph), write the ratio as a fraction and divide: 20/2 = 20 ÷ 2 = 10. This means that you're riding your bike at a speed of 10 mph if you cover 20 miles every 2 hours.

Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Elementary Math Help: 5th and 6th Grade

    Mathematics classes get increasingly difficult towards the end of elementary school. Learn how to help your fifth and sixth grade students improve their math skills.

  • More Blog Articles
    MIND Games Lead to Math Gains

    Imagine a math teaching tool so effective that it need only be employed twice per week for less than an hour to result in huge proficiency gains. Impossible, you say? Not so...and MIND Research Institute has the virtual penguin to prove it.

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online

K12

  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only

Kumon

  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only

TutorVista

  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Help Your Child Succeed

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth