A Ratio is a comparison of two quantities. Equivalent ratios are two ratios that express that same relationship between two numbers. Part to Part and Part to Whole. Look at the equivalent ratios below. There are two types of ratios. © 2021 Divide and Calculate Double number lines can be used to solve ratio problems. They are used to visualize the relationship between two quantities. What number was multiplied by the first A part to part ratio compares one part ratio to create the second ratio? That to another part. number is called the scale factor. A part to whole ratio compares one part to the whole. 4/5=8/10 1/2=5/10 The circle below has four pieces. Each piece is one part of the whole shape. A 3/8=9/24 8/9=56/63 We can scale up using the scale factor and multiplication. We can scale down using the scale factor and division. tape diagram is a drawing that Benchmark Percents are commonly used percents that may help in estimating or solving percent problems. looks like a piece of tape. It can be used to help solve a ratio problem. This tape diagram shows the ratio of __________ to __________ in a fruit salad. There are 3 different methods we can use to divide fractions. 1. Find a common denominator. Use the common denominator 36 to solve. 20/36 ÷ 9/36 = 20/9 2. Divide denominators. The word percent means parts per hundred. A percent is a fraction expressed as a number of hundredths. For example, one hundredth, written as a decimal 0.01, or as a fraction 1/100, can also be expressed as numerators and A Change 2/3 to Use number lines, ratio tables, or pictures to solve ratio reasoning problems. 1%. percent bar is a model used to You can also solve a percent problem using equivalent ratios. What is 30% of 50? Steps for Long Division solve percent problems. Divide the equivalent 12/18. 12/18 ÷ 1/6 = 12/3 3. Multiply Multiply by the reciprocal Subtract Flip the second fraction and change to multiplication. Bring Down 7/8 x 3/1 = 21/8 When dividing fractions, you may notice that a/b ÷ c/d = a/b x d/c The greatest common factor is the largest factor shared by two or more numbers. Factors of 12: Factors of 16: 1, 2, 3, 4, 6, 12 1, 2, 4, 8, 16 Repeat/Remainder Factor Trees are useful to find factors and determine the prime factorization of a number. The number line consists of positive and negative integers. An integer is a positive or negative whole number, or zero. The prime factorization of 48 is 2x2x2x2x3 or The LCM of two numbers a and b, is the smallest number that is divisible by both a and b. There are two methods for finding the LCM. We can find the LCM of 9 and 12 using the two different methods. Decimals . Customary Length 1 ft. = 12 in. 1 yd. = 3 ft. 1 mi. = 5280 ft. 1 mi. = 1760 yds. Customary Volume 1 gal. = 4 qt. 1 gal. = 128 oz. 1 qt. = 2 pts. 1 pt. = 2 c. 1 c. = 8 oz. Metric Length 1 km. = 1000 m. 1 m. = 100 cm. 1 cm. = 10 mm. Metric Volume 1 liter = 1000 milliliters 6th Grade Math Quick Reference Guide Perimeter of a rectangle = 2l + 2w Surface Area = Add area of all faces deviation is the average of the deviations from the mean. The MAD can be found by adding together all of the deviations, then dividing by the number of values. Absolute Deviation. The (MAD) mean absolute Finding the Mean A histogram is a graphical representation showing the distribution of numerical data using bars of different heights. Absolute value is the distance a number is from zero. The coordinate plane is formed by a horizontal line called the x-axis and a vertical line called the y-axis. It is divided into four quadrants The origin is located at point (0,0). An ordered pair is used to plot a point on the plane. The first number is the x coordinate and the second number is the y coordinate (x, y). Expressions are mathematical sentences that may use variables, numbers, and operations. Expressions that contain a variable are known as algebraic expressions. π +6y+5x+12, the variables are x and y. A variable is In the expression π a letter used to represent a number. The term 6y has a coefficient of 6. 12 In the expression, the number is called a constant. This number does not change. In the expression, π₯2 contains the exponent 2. This represents x β x. -2 is 2 units away from zero. 3 is 3 units away from zero. The Order of Operations is the sequence of mathematical operations that must be followed when evaluating expressions. 1 P arentheses ( ) You can write an expression from a description that uses words. 2 βFor example, six more than 3 can be written as 3 + 6. βAn expression, seven less than Y can be written as 9 4 Y – 7. βUsing multiplication, the product of 6 and P can be written as 6P. β Using division, nine divided by Z, can be written as 9 ÷ Z, or π 3 When solving equations, we must perform certain steps to isolate the variable by itself on one side of the equal sign. xponents π₯3 ultiply β ivide ÷ dd + ubtract _ We can use algebra tiles to represent an expression, . An equation is a mathematical statement of equality between two expressions. E M D A S An inequality is the relation between two expressions when they are not equal. We use symbols to show inequality in math. 3(x+3). The volume of a rectangular prism can be found using the formula V= l x w x h. Volume is the amount of space an object occupies. You can think of volume as the amount of space within a container. Volume = length x width x height V= 6cm x 4cm x 5cm V= 120 πππ We can do the opposite of the constant (add or subtract) or the opposite of the coefficient (multiply or divide), to help in isolating the variable. The area of a regular polygon can be found by using a specific formula for each shape. Statistics is the study and analysis of data collection. A statistical question is an inquiry that collects data with some degree of variability. These are statistical questions: 1. How many minutes do sixth graders study each week? 2. What were the student scores on the math test? These are non-statistical questions: 1. How many minutes did Dave watch television yesterday? 2. How many days are in January? A measure of center is a numerical value that describes the central position of a data set. Mean, median, mode, and range are used to analyze a data set. The mean is the average of a data set. It can be determined by adding all of the values and then dividing by the number of values. The median is the middle value of a data set. It can be determined by putting the values in order and finding the middle point. When the middle point is between two values, they can be averaged to find the middle value. A box plot is a graphic that shows statistical data plotted using the five number summary (minimum, lower quartile, median, upper quartile, and maximum). The mode is the value that occurs most often in the set. The range can be found by subtracting the least value from the greatest value in the data set. A dot plot is a graphic that shows statistical data plotted as dots. © 2021 Divide and Calculate
