A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a=a1+

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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?

Mathematics

2 answers:

Inessa [12.5K] · Answer 1 · 2026-02-17T18:03:19+03:00

Answer:

Identify the least common multiple of the denominators found within the equation.

Explanation:

To solve this problem, you need to determine the least common multiple (LCM) of the denominators before adding the fractions.

Detailed explanation:

The given expression is,

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

Where,

a represents the acceleration of the object, which we aim to find.

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

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

m = 7.00 kg

By plugging in these values, the equation is rewritten as,

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

The two values to be combined are 12/7 and 3; one is a fraction and the other is a whole number.

Adding these requires finding a shared denominator, which lies beneath the division line in a fraction.

For 12/7, the denominator is 7; for 3, considered as 3/1, the denominator is 1.

To find a common denominator for these fractions, calculate the least common multiple of 7 and 1.

The least common multiple is the smallest number divisible by both denominators fully.

Here, the LCM is 7.

Thus, 7 becomes the common denominator.

Look at $\dfrac{12}{7}$ . Since its denominator is already 7, no changes are needed.

For 3, convert the denominator from 1 to 7 by multiplying the denominator by 7, and also multiply the numerator by 7.

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

Now that the denominators match, we can sum the fractions like this,

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

Hence, the result 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

Leona [12.6K] · Answer 2 · 2026-02-17T18:04:09+03:00

Answer:

$a=\frac{3\times 7}{7}+\frac{12}{7}$ (The initial step to find a common denominator between the two fractions)

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

Detailed explanation:

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

where,

a is the acceleration of the object (to be calculated)

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

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

$m=7.00\text{ kg}$

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

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

Next, we simplify the equation for a.

We start by finding a common denominator.

The common denominator is 7. So, both fractions are converted to have denominator 7 by multiplying numerator and denominator of the fraction with 3 by 7.

$a=\frac{3\times 7}{7}+\frac{12}{7}$ (The first step to get a common denominator for the fractions)

We then add the numerators together.

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

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