How can you convert among fractions, decimals, and percents

Step-by-step explanation:

Changing Percents to Decimals

The word percent means "per 100."  20% means 20 out of 100, or 20/100.   67% means 67 out of 100, or 67/100.  So to change a percent to a decimal, you simply divide the percentage number by 100.  When you divide by 100, the decimal just moves over 2 places to the left.

Changing Percents to Fractions

Remember, the word percent means "per 100."  This means you can change a percent to a fraction by dividing by 100.  Don't stop here though, make sure to simplify the fraction if possible.  Look to see if the numerator and denominator can be divided by the same number.

Changing Decimals to Fractions

First, figure out the place value of the last digit on the right.  Is it in the tenths place? Hundredths? Thousandths?  Use the place value to write the decimal as a fraction over 10, 100, 1000, etc. Then simplify the fraction if possible.

Remember, the first place to the right of the decimal is the tenths place.  The second place is the hundredths, then thousandths, ten thousandths, and so on.  

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.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b