This is a couple of my childs homework, can anyone help me? I want to be able to check if he did it correctly.

1.

112 miles is double 56 miles. The car will need double the gasoline. That’s 8 gallons.

Formally, the calculation would be written 112 * 4 / 56.

You then cancel the 56 into the 112 giving 2, which multiplies by 4 to give 8.

2.

(m^6 / 6) / (m^8 / 30)

Change the middle division sign to multiply, and invert the fraction in the second bracket. That gives:

( m^6 / 6) * (30 / m^8)

Now resequence the multiplications before the divisions:

(30m^6) / (6m^8)

Divide the 6 into the 30 giving 5 on top.

Divide m^6 into m^8 giving m^2 below.

Result 5 / m^2.

1. 4 / 56 = 14

112 /14 = 8 gallons of gasoline

2. I’m not sure what you are asking. I think you are trying to simplfy the fraction. 6/6 =1 and 8/30= 4/15

1) 4 gallons for every 56 miles… 112 miles is twice of 56 miles. Thus, you need double of the gas.

ANSWER: 8 gallons

2) If you mean this [m^(6/6)] / [m^(8/30)]

Division of exponential numbers with same base (eg: m) just subtracts the exponents, so (6/6)-(8/30)=(22/30) or (11/15)

ANSWER: m^(11/15)

1. Set up a proportion and solve.

4/56 = x/112 (read 4 is to 56 as x is to 12)

Now cross multiply and get: 56x = 112*4 or 56x=448. Now solve for x by dividing 448 by 56 and get x= 8 gallons.

2. This is simplifying exponents.

m^6/6 / m^8/30

First when dividing by a fraction, you need

multiply by the reciprocal (just flip the 2nd fraction and multiply), so you have m^6/6 * 30/m^8. Now multiply and get 30m^6/6m^8.

Now divide and get 5m^-2. Finally, simplify by bringing the negative exponent to the bottom of the fraction and make it positive and you have 5/m^2. I know this sounds confusing, you may want to review rules of simplifying exponents.

first part…

1. 56 miles = 4 gallons

112miles = 56 x 2 …. 2 x 4 = 8 gallons

2. M^22/30

i think this is the answer to number 2…kinda tricky to work and put it in the answer box…

1. 8 gallons.

2. I do not understand the question…sorry.

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