# Tutor profile: Anna B.

## Questions

### Subject: Pre-Algebra

How do I solve an algebraic equation with one variable?

Let's work with this example: 25 = 5 + 5x When we're working with an equation, we want to remember to do the same thing to both sides of the equation (both sides of the = sign). We're trying to solve for x, meaning we need to figure out what value the variable x represents. In order to do that, we need to isolate the variable. When we've solved the equation, x will be on one side of the equation (one side of the = sign) and the value of x will be on the other side. First, identify like terms. 5 and 5x are not like terms. We can't simplify the equation by adding them together. But, 25 and 5 are like terms. If we moved 5 to the other side of the equation, 25 and 5 could be combined to simplify the equation. If we subtract 5 from both sides of the equation, it brings the 5 from the right side of the equation to the left side. 25 − 5 = 5 + 5x − 5 Like we said before, 5 can be subtracted from 25, because they are like terms. The 5 on the right side of the equation is canceled out. 20 = 5x We're a step closer to isolating x. 5 is a coefficient of the variable x. 5 and x are attached by multiplication. In order to separate them, we have to do the inverse of multiplication – division. Since we have to do the same thing to both sides of the equation, let's divide both sides by 5. 20 ÷ 5 = 5x ÷ 5 4 = x We've finished solving the equation. The value of x is 4.

### Subject: Basic Math

How do you divide a fraction by another fraction?

Let's say you have this problem: $$ \frac{4}{5} $$ ÷ $$ \frac{3}{4} $$ Dividing fractions looks intimidating, but with one simple step, it becomes a multiplication problem. When you're dividing two fractions, flip the second fraction by switching the numerator and the denominator, and change the division symbol to a multiplication symbol. $$ \frac{4}{5} $$ ÷ $$ \frac{3}{4} $$ becomes $$ \frac{4}{5} $$ × $$ \frac{4}{3} $$ Then, you can multiply across the numerator and the denominator, like you've done to multiply fractions before. $$ \frac{4}{5} $$ × $$ \frac{4}{3}$$ = $$ \frac{16}{15} $$ Our numerator and denominator don't share any common factors, so we can't simplify this fraction any further, but, we can represent it as a mixed number. $$ \frac{16}{15} $$ = 1 $$ \frac{1}{15} $$

### Subject: English

What is the difference between an adjective and an adverb?

Adjectives modify, or describe, nouns or pronouns. Adverbs modify, or describe, verbs, adjectives, or other adverbs. Adverbs answer questions like how, why, where, when, and to what extent. Let's think of an example: He threw the red ball. In this sentence, "ball" is a noun. "Red" describes the color of the ball. The word "red" modifies the word "ball." Since "ball" is a noun, and "red" modifies it, then "red" is an adjective. Let's add another layer to this same example: He threw the dark red ball. "Ball" is still a noun, and "red" still modifies it, so "red" is still an adjective. We've added the word "dark," which is describing the color red. How red is the ball? It's dark red. "Dark" is an adverb modifying the adjective "red." Got it so far? Let's think through two more examples. He threw the bouncy, red ball. In this case, bouncy and red both describe the ball. This means they're both adjectives. Last one! He quickly threw the red ball. How did he throw the ball? Quickly. "Threw" is a verb and "quickly" modifies it, which means quickly is an adverb.

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