Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following addition, giving the fraction in its simplest form.
", "advice": "$\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}+\\frac{\\var{c_coprime}}{\\var{d_coprime}}$
\nTo add or subtract fractions, we need to have a common denominator on both fractions.
\nTo get a common denominator, we need to find the lowest common multiple of the two denominators.
\nThe lowest common multiple of $\\var{b_coprime}$ and $\\var{d_coprime}$ is $\\var{lcm}.$
\nThis will be the new denominator, and we need to multiply each fraction individually to ensure we get this denominator.
\nFor $\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}$, we need to multiply the fraction by $\\displaystyle\\frac{\\var{lcm_b}}{\\var{lcm_b}}$ to give $\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}.$
\nFor $\\displaystyle\\frac{\\var{c_coprime}}{\\var{d_coprime}}$, we need to multiply the fraction by $\\displaystyle\\frac{\\var{lcm_d}}{\\var{lcm_d}}$ to give $\\displaystyle\\frac{\\var{clcm_d}}{\\var{lcm}}.$
\nNow that we have each fraction in terms of a common denominator, we can now add the fractions together.
\n$\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}+\\frac{\\var{clcm_d}}{\\var{lcm}}=\\frac{(\\var{alcm_b}+\\var{clcm_d})}{\\var{lcm}}=\\frac{\\var{alcmclcm}}{\\var{lcm}}.$
\nFrom this, we can try to simplify the result down by finding the greatest common divisor of the numerator and denominator and dividing the whole fraction by this amount.
\nThe greatest common divisor of $\\var{alcmclcm}$ and $\\var{lcm}$ is $\\var{gcd}.$
\nSimplifying using this value gives a final answer of $\\displaystyle\\frac{\\var{num}}{\\var{denom}}.$
\nTherefore, the expression cannot be simplified further, and $\\displaystyle\\frac{\\var{num}}{\\var{denom}}$ is the final answer.
\n\nFind out more about this topic using our resource
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