Question

A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a=a1+Fm where a1=3.00 meter/second2, F=12.0kilogram⋅meter/second2 and m=7.00kilogram. First, which of the following is the correct step for obtaining a common denominator for the two fractions in the expression in solving for a?

Answer 1

Answer:

Least common multiple of the denominators in the equation should be found.

Explanation:

To solve this question the least common multiple of the denominators should be found to add them.

Further explanation:

Given expression is,

$a = a_{1} + \frac{F}{m}$

Where,

a is acceleration of an object.(which is needed to be calculated)

$a_{1} = 3.00 m s^{-2}$

$F = 12.0 \ kg\cdot m s^{-2}$

m = 7.00 kg

once the values are substituted, the above equation can be expressed as,  

$a = 3 + \dfrac{12}{7}$

The given values that should be added are 12/7 & 3. One of them is a fraction & other value is an integer.

To get the summation the common denominator of the fractions should be found. Denominator is the number under the division symbol.

So the denominator of 12/7 is 7. The denominator of 3 is 1.  (all integers has denominator 1)

To find the common denominator of given fractions, the least common multiple of 7 & 1 should be found.

Least common multiple is the lowest number that both 7 & 1 are fully divided.

So the least common multiple is 7.

Therefore, the common denominator is 7.

• Consider $\dfrac{12}{7}$. There is no conversion as the denominator is already 7.  

• Consider 3. To convert the denominator 1 to 7, 1 should be multiplied by 7. Therefore the numerator, 3 also should be multiplied by 7. (Numerator is the upper part of the fraction)

$\dfrac{3\times 7}{1\times 7} = \dfrac{21}{7}$

Now we have converted the given fractions to a common denominator. Then we can add them as,

$\dfrac{12}{7}+\dfrac{21}{7}=\dfrac{33}{7}$

So the answer is,  

$a=\dfrac{33}{7} \ m/s^2}$

Learn more:

1. brainly.com/question/513185, Answered by Evadin2019

Keywords

Least common multiple, denominator numerator, fraction

Answer 2

Answer:

$a=\frac{3\times 7}{7}+\frac{12}{7}$  (First step for obtaining a common denominator for the two fraction)

$a=\frac{33}{7}\text{ m/s}^2$

Step-by-step explanation:

$\text{Given Expression: }a=a_1+\frac{F}{m}$

where,

a is acceleration of an object.(Need to calculate)

$a_1=3.00\text{ m/s}^2$

$F=12.0\text{ Kg.m/s}^2$

$m=7.00\text{ kg}$

$\text{Substitute }a_1, \text{ F, and m into expression and we get}$

$a=3+\frac{12}{7}$

Now we will simplify above expression for a

First we make common denominator.

Common denominator is 7. So, we make both denominator 7. We multiply by 7 at top and bottom with 3. We get

$a=\frac{3\times 7}{7}+\frac{12}{7}$  (First step for obtaining a common denominator for the two fraction)

Now we combine the numerator

$a=\frac{21+12}{7}$

$a=\frac{33}{7}\text{ m/s}^2$