Seven more than the product of a number and three is equal to four

First, write this out as an equation

"Seven more" means 7 plus something. "the product of a number and three" Product means multiply and the "a number", we don't know that number. So use a variable (we'll use x) to represent it. "is equal to four" pretty straight forward. = 4. Okay, let's write this out:

7 + x3 = 4

3 is written right next to x (with no space) to indicate multiplication. Now we need to solve this. Let's get x by itself on the left side of the equal sign. Start by subtracting 7 from BOTH sides.

7-7 = 0 (we dont write the zero) and 4 - 7 = -3.

So now we have;

x3 = -3

x still isn't by itself. 3 is still stuck to it, so let's undo that. Since 3 is being multiplied by x, DIVIDE it.

x3 divided by 3 = x. -3 divided by 3 = -1.

So, x = -1.

To make sure this is true, substitute -1 in for x.

7 + (-1)3 = 4

(USE ORDER OF OPERATIONS!)

7 + -3 = 4 (-1 * 3 = -3)

4 = 4 (7 + -3 is the same as 7 - 3, which is 4. 4 = 4 , so this is correct!)

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.