7th grade math worksheets
Practice 7th grade algebra with two-step equations, expansion and collection of like terms, and factoring out the greatest common factor.
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Addition & subtraction 5 skills
- Adding signed fractions and decimals Use a common denominator for fractions and align decimal places. A minus sign before a mixed number applies to the whole value.
- Distance and displacement Signed change is end minus start. Distance is the absolute value of the change.
- Opposites and zero pairs Opposites have equal magnitudes and opposite signs. Their sum is zero.
- Signed addition on number lines Start + change = end. Positive change moves right or up; negative change moves left or down.
- Subtracting signed fractions and decimals Keep the first number and add the opposite of the second. A minus sign before a mixed number applies to the whole value.
Ratios & percents 9 skills
- Comparing rates with conversions Convert both rates to the same units. Square the length conversion factor for area, and check the direction of each conversion.
- Finding the constant across representations Divide output by input to find the unit rate. Check that both supplied views give the same rate.
- Fractional unit rates Use the requested units to decide which quantity to divide by which. Multiply by the reciprocal and keep the units.
- Graphing proportional relationships A proportional graph is a straight line through the origin. Read each coordinate using its axis label.
- Interpreting proportional graph points A proportional graph is a straight line through the origin. Read each coordinate using its axis label.
- Multistep ratio applications Keep each quantity attached to its units. A ratio between two parts uses a different base from a part of the whole.
- Proportionality in graphs A proportional graph is a straight line through the origin. Read each coordinate using its axis label.
- Proportionality in tables Check that zero input gives zero output, then compare cross products of the nonzero pairs.
- Writing proportional equations Find the output per one input unit. Multiply the input quantity by that rate to get the output quantity.
Expressions & equations 15 skills
- Adding linear expressions Remove the parentheses without changing signs. Combine like terms.
- Checking contextual solutions Substitute into the original model. A solution must make it true and fit the quantity and its units.
- Collecting rational like terms Add the coefficients of like terms. Use a common denominator to add fractions.
- Collecting terms and constants Combine the variable terms and constants separately. Use common denominators for fractions.
- Expanding and collecting like terms Multiply each term inside the parentheses by the outside factor. Then combine like terms.
- Expanding with rational factors Multiply each term inside the parentheses by the outside factor.
- Factoring out a specified rational factor Divide each term by the given factor. Keep that factor outside the parentheses, then expand to check.
- Factoring out the greatest common factor Find the greatest positive integer that divides both coefficients. Factor it out, then expand to check.
- Graphing inequality solution sets Use an open circle for < or > and a closed circle for ≤ or ≥. Shade toward the values that satisfy the inequality.
- Solving grouped equations Divide both sides by the factor outside the parentheses. Then undo the addition or subtraction.
- Solving inequalities with negative coefficients Adding or subtracting preserves the direction. Dividing by a negative number reverses it.
- Solving inequalities with positive coefficients Adding or subtracting preserves the direction. Dividing by a positive number also preserves it.
- Solving two-step equations Undo the addition or subtraction first. Then divide both sides by the coefficient.
- Subtracting grouped linear expressions Subtract every term in the second group, then combine like terms.
- Writing equations from quantities Define the unknown and its units. Repeated quantity plus fixed amount equals the total.
About 7th grade math
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