Common Core: 7th Grade Math : Ratios & Proportional Relationships

Example Questions

Example Question #81 : Grade 7

Megan can clean  of a house in  of an hour. If she continues at this rate, how much of the house can Megan clean per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the house, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Megan can clean  of the house per hour.

Example Question #82 : Grade 7

Armen can complete  of his homework in  of an hour. If he continues at this rate, how much of his homework can Armen complete per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have amount of homework, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Armen can complete  of his homework per hour.

Example Question #83 : Grade 7

A baker can decorate  of a wedding cake in  of an hour. If the baker continues this at rate, how much of the wedding cake can he decorate per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the cake decorated, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

The baker can decorate  of the wedding cake per hour.

Example Question #81 : Grade 7

A painter can paint  of a house in  of an hour. If he continues at this rate, how much of the house can he paint per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have portion of the house painted, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

The painter can paint  of a house per hour.

Example Question #82 : Grade 7

A janitor can clean  of a stadium in  of an hour. If he continues at this rate, how much of the stadium can he clean per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the stadium, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

The janitor can clean  of the stadium per hour.

Example Question #86 : Grade 7

Andrew spends every Saturday at the gym working out. He can complete  of his workout in  of an hour. If he continues at this rate, how much of his workout does Andrew complete per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of his workout, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Andrew can complete  of his workout per hour.

Example Question #87 : Grade 7

Andrew spends every Saturday at the gym working out. He can complete  of his workout in  of an hour. If he continues at this rate, how much of his workout does Andrew complete per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of his workout, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Andrew can complete  of his workout per hour.

Example Question #87 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Eric walks one-fourth of a mile in half an hour. If he continues at this rate, what is Eric's speed in miles per hour

Explanation:

The phrase "miles per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have miles, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Eric can walk at a speed of:

Example Question #1 : Rational Numbers

In a class of  students, the ratio of freshmen to sophomores to juniors is . How many juniors are in the class?

Explanation:

Let  be the number of freshmen,  be the number of sophomores, and  be the number of juniors.

Now, since we have  students,

Since we want to find the number of juniors, we need to find the value of .

Example Question #1 : Rational Numbers

In a zoo with  animals, the ratio of mammals to reptiles to birds is . How many birds does the zoo have?

Explanation:

Let  be the number of mammals, be the number of reptiles, and  be the number of birds.

Since the zoo has  animals,

Because we want the number of birds, we need to find the value of .