Virginia SOL Math / Grade 7 / Computation & Estimation

7.CE.1

Multistep Problems with Rational Numbers

What you'll learn

  • Add, subtract, multiply, and divide rational numbers, including negatives
  • Apply the order of operations to rational number expressions
  • Solve multistep problems in context

Words to know

Rational number —
any number that can be written as a fraction of two integers
Order of operations —
the agreed order: grouping, exponents, multiply and divide, then add and subtract
Reciprocal —
the number you multiply by to get 1, found by flipping a fraction
Absolute value —
the distance of a number from zero
Multistep —
a problem that takes more than one operation to solve

Why it matters Real situations often mix positive and negative amounts and several steps, such as tracking a bank balance or a change in temperature over time.

Worked examples

Model ItI do

Find negative 3 + 5 times 2.

Follow the order of operations: multiply first, 5 times 2 = 10. Then add: negative 3 + 10 = 7.

Try It TogetherWe do

Find one half divided by negative 2.

Dividing means multiply by the reciprocal of negative 2, which is negative one half. So one half times negative one half = negative one fourth.

Now YouYou do

The temperature was 4 degrees, then dropped 9 degrees, then rose 2 degrees. What is the final temperature?

Add and subtract in order from left to right. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find negative 6 + 10.

  2. 2.Find negative 3 times 4.

  3. 3.Find 20 divided by negative 5.

On Level

The core Quick Check from the book.

  1. 1.Find negative 7 + 12.

  2. 2.Find negative 4 times negative 6.

  3. 3.Find 8 divided by negative 2.

  4. 4.Find 3 + 2 times 5.

  5. 5.A diver at negative 15 feet rises 6 feet. What is the new depth?

Challenge

Stretch your thinking.

  1. 1.Find negative 2 + 3 times negative 4.

  2. 2.Find negative 3 over 4 minus 1 over 2.

  3. 3.A submarine at negative 40 feet dives 25 more feet, then rises 18 feet. What is its final depth?